You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
592 lines
20 KiB
Fortran
592 lines
20 KiB
Fortran
!!$
|
|
!!$ Parallel Sparse BLAS version 3.0
|
|
!!$ (C) Copyright 2010
|
|
!!$ Salvatore Filippone University of Rome Tor Vergata
|
|
!!$ Alfredo Buttari CNRS-IRIT, Toulouse
|
|
!!$
|
|
!!$ Contributions to this routine:
|
|
!!$ Daniela di Serafino Second University of Naples
|
|
!!$ Pasqua D'Ambra ICAR-CNR
|
|
!!$
|
|
!!$ Redistribution and use in source and binary forms, with or without
|
|
!!$ modification, are permitted provided that the following conditions
|
|
!!$ are met:
|
|
!!$ 1. Redistributions of source code must retain the above copyright
|
|
!!$ notice, this list of conditions and the following disclaimer.
|
|
!!$ 2. Redistributions in binary form must reproduce the above copyright
|
|
!!$ notice, this list of conditions, and the following disclaimer in the
|
|
!!$ documentation and/or other materials provided with the distribution.
|
|
!!$ 3. The name of the PSBLAS group or the names of its contributors may
|
|
!!$ not be used to endorse or promote products derived from this
|
|
!!$ software without specific written permission.
|
|
!!$
|
|
!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
|
!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
|
|
!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
|
|
!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS
|
|
!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
|
|
!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
|
|
!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
|
!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
|
|
!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
|
|
!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
|
!!$ POSSIBILITY OF SUCH DAMAGE.
|
|
!!$
|
|
!!$
|
|
!!$ CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
|
|
!!$ C C
|
|
!!$ C References: C
|
|
!!$ C [1] Duff, I., Marrone, M., Radicati, G., and Vittoli, C. C
|
|
!!$ C Level 3 basic linear algebra subprograms for sparse C
|
|
!!$ C matrices: a user level interface C
|
|
!!$ C ACM Trans. Math. Softw., 23(3), 379-401, 1997. C
|
|
!!$ C C
|
|
!!$ C C
|
|
!!$ C [2] S. Filippone, M. Colajanni C
|
|
!!$ C PSBLAS: A library for parallel linear algebra C
|
|
!!$ C computation on sparse matrices C
|
|
!!$ C ACM Trans. on Math. Softw., 26(4), 527-550, Dec. 2000. C
|
|
!!$ C C
|
|
!!$ C [3] M. Arioli, I. Duff, M. Ruiz C
|
|
!!$ C Stopping criteria for iterative solvers C
|
|
!!$ C SIAM J. Matrix Anal. Appl., Vol. 13, pp. 138-144, 1992 C
|
|
!!$ C C
|
|
!!$ C C
|
|
!!$ C [4] R. Barrett et al C
|
|
!!$ C Templates for the solution of linear systems C
|
|
!!$ C SIAM, 1993 C
|
|
!!$ C C
|
|
!!$ C C
|
|
!!$ C [5] G. Sleijpen, D. Fokkema C
|
|
!!$ C BICGSTAB(L) for linear equations involving unsymmetric C
|
|
!!$ C matrices with complex spectrum C
|
|
!!$ C Electronic Trans. on Numer. Analysis, Vol. 1, pp. 11-32, C
|
|
!!$ C Sep. 1993 C
|
|
!!$ C C
|
|
!!$ C C
|
|
!!$ CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
|
|
! File: psb_crgmres.f90
|
|
!
|
|
! Subroutine: psb_crgmres
|
|
! This subroutine implements the restarted GMRES method with right
|
|
! preconditioning.
|
|
!
|
|
! Arguments:
|
|
!
|
|
! a - type(psb_c_sparse_mat) Input: sparse matrix containing A.
|
|
! prec - class(psb_cprec_type) Input: preconditioner
|
|
! b - complex,dimension(:) Input: vector containing the
|
|
! right hand side B
|
|
! x - complex,dimension(:) Input/Output: vector containing the
|
|
! initial guess and final solution X.
|
|
! eps - real Input: Stopping tolerance; the iteration is
|
|
! stopped when the error estimate |err| <= eps
|
|
! desc_a - type(psb_desc_type). Input: The communication descriptor.
|
|
! info - integer. Output: Return code
|
|
!
|
|
! itmax - integer(optional) Input: maximum number of iterations to be
|
|
! performed.
|
|
! iter - integer(optional) Output: how many iterations have been
|
|
! performed.
|
|
! performed.
|
|
! err - real (optional) Output: error estimate on exit. If the
|
|
! denominator of the estimate is exactly
|
|
! 0, it is changed into 1.
|
|
! itrace - integer(optional) Input: print an informational message
|
|
! with the error estimate every itrace
|
|
! iterations
|
|
! istop - integer(optional) Input: stopping criterion, or how
|
|
! to estimate the error.
|
|
! 1: err = |r|/|b|; here the iteration is
|
|
! stopped when |r| <= eps * |b|
|
|
! 2: err = |r|/(|a||x|+|b|); here the iteration is
|
|
! stopped when |r| <= eps * (|a||x|+|b|)
|
|
! where r is the (preconditioned, recursive
|
|
! estimate of) residual.
|
|
! irst - integer(optional) Input: restart parameter
|
|
!
|
|
Subroutine psb_crgmres(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,irst,istop)
|
|
use psb_sparse_mod
|
|
use psb_prec_mod
|
|
use psb_inner_krylov_mod
|
|
use psb_krylov_mod
|
|
implicit none
|
|
|
|
!!$ Parameters
|
|
Type(psb_c_sparse_mat), Intent(in) :: a
|
|
class(psb_cprec_type), Intent(in) :: prec
|
|
Type(psb_desc_type), Intent(in) :: desc_a
|
|
complex(psb_spk_), Intent(in) :: b(:)
|
|
complex(psb_spk_), Intent(inout) :: x(:)
|
|
Real(psb_spk_), Intent(in) :: eps
|
|
integer, intent(out) :: info
|
|
Integer, Optional, Intent(in) :: itmax, itrace, irst,istop
|
|
Integer, Optional, Intent(out) :: iter
|
|
Real(psb_spk_), Optional, Intent(out) :: err
|
|
!!$ local data
|
|
complex(psb_spk_), allocatable, target :: aux(:),w(:),w1(:), v(:,:)
|
|
complex(psb_spk_), allocatable :: c(:),s(:), h(:,:), rs(:),rst(:),xt(:)
|
|
Real(psb_spk_) :: tmp
|
|
complex(psb_spk_) :: rti, rti1, scal
|
|
Integer ::litmax, naux, mglob, it,k, itrace_,&
|
|
& np,me, n_row, n_col, nl, int_err(5)
|
|
Logical, Parameter :: exchange=.True., noexchange=.False.
|
|
Integer, Parameter :: irmax = 8
|
|
Integer :: itx, i, isvch, ictxt,istop_, err_act
|
|
integer :: debug_level, debug_unit
|
|
Real(psb_dpk_) :: rni, xni, bni, ani,bn2
|
|
real(psb_dpk_) :: errnum, errden, deps, derr
|
|
character(len=20) :: name
|
|
character(len=*), parameter :: methdname='RGMRES'
|
|
|
|
info = psb_success_
|
|
name = 'psb_cgmres'
|
|
call psb_erractionsave(err_act)
|
|
debug_unit = psb_get_debug_unit()
|
|
debug_level = psb_get_debug_level()
|
|
|
|
ictxt = psb_cd_get_context(desc_a)
|
|
Call psb_info(ictxt, me, np)
|
|
if (debug_level >= psb_debug_ext_)&
|
|
& write(debug_unit,*) me,' ',trim(name),': from psb_info',np
|
|
|
|
mglob = psb_cd_get_global_rows(desc_a)
|
|
n_row = psb_cd_get_local_rows(desc_a)
|
|
n_col = psb_cd_get_local_cols(desc_a)
|
|
|
|
if (present(istop)) then
|
|
istop_ = istop
|
|
else
|
|
istop_ = 2
|
|
endif
|
|
!
|
|
! ISTOP_ = 1: Normwise backward error, infinity norm
|
|
! ISTOP_ = 2: ||r||/||b||, 2-norm
|
|
!
|
|
|
|
if ((istop_ < 1 ).or.(istop_ > 2 ) ) then
|
|
info=psb_err_invalid_istop_
|
|
int_err(1)=istop_
|
|
err=info
|
|
call psb_errpush(info,name,i_err=int_err)
|
|
goto 9999
|
|
endif
|
|
|
|
if (present(itmax)) then
|
|
litmax = itmax
|
|
else
|
|
litmax = 1000
|
|
endif
|
|
|
|
if (present(itrace)) then
|
|
itrace_ = itrace
|
|
else
|
|
itrace_ = 0
|
|
end if
|
|
|
|
if (present(irst)) then
|
|
nl = irst
|
|
if (debug_level >= psb_debug_ext_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' present: irst: ',irst,nl
|
|
else
|
|
nl = 10
|
|
if (debug_level >= psb_debug_ext_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' not present: irst: ',irst,nl
|
|
endif
|
|
if (nl <=0 ) then
|
|
info=psb_err_invalid_istop_
|
|
int_err(1)=nl
|
|
err=info
|
|
call psb_errpush(info,name,i_err=int_err)
|
|
goto 9999
|
|
endif
|
|
|
|
call psb_chkvect(mglob,1,size(x,1),1,1,desc_a,info)
|
|
if(info /= psb_success_) then
|
|
info=psb_err_from_subroutine_
|
|
call psb_errpush(info,name,a_err='psb_chkvect on X')
|
|
goto 9999
|
|
end if
|
|
call psb_chkvect(mglob,1,size(b,1),1,1,desc_a,info)
|
|
if(info /= psb_success_) then
|
|
info=psb_err_from_subroutine_
|
|
call psb_errpush(info,name,a_err='psb_chkvect on B')
|
|
goto 9999
|
|
end if
|
|
|
|
|
|
naux=4*n_col
|
|
allocate(aux(naux),h(nl+1,nl+1),&
|
|
&c(nl+1),s(nl+1),rs(nl+1), rst(nl+1),stat=info)
|
|
|
|
if (info == psb_success_) Call psb_geall(v,desc_a,info,n=nl+1)
|
|
if (info == psb_success_) Call psb_geall(w,desc_a,info)
|
|
if (info == psb_success_) Call psb_geall(w1,desc_a,info)
|
|
if (info == psb_success_) Call psb_geall(xt,desc_a,info)
|
|
if (info == psb_success_) Call psb_geasb(v,desc_a,info)
|
|
if (info == psb_success_) Call psb_geasb(w,desc_a,info)
|
|
if (info == psb_success_) Call psb_geasb(w1,desc_a,info)
|
|
if (info == psb_success_) Call psb_geasb(xt,desc_a,info)
|
|
if (info /= psb_success_) then
|
|
info=psb_err_from_subroutine_non_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
end if
|
|
if (debug_level >= psb_debug_ext_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' Size of V,W,W1 ',size(v),size(v,1),&
|
|
& size(w),size(w,1),size(w1),size(w1,1), size(v(:,1))
|
|
|
|
! Ensure global coherence for convergence checks.
|
|
call psb_set_coher(ictxt,isvch)
|
|
|
|
if (istop_ == 1) then
|
|
ani = psb_spnrmi(a,desc_a,info)
|
|
bni = psb_geamax(b,desc_a,info)
|
|
else if (istop_ == 2) then
|
|
bn2 = psb_genrm2(b,desc_a,info)
|
|
endif
|
|
errnum = dzero
|
|
errden = done
|
|
deps = eps
|
|
if (info /= psb_success_) then
|
|
info=psb_err_from_subroutine_non_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
end if
|
|
if ((itrace_ > 0).and.(me == 0)) call log_header(methdname)
|
|
|
|
itx = 0
|
|
restart: do
|
|
|
|
! compute r0 = b-ax0
|
|
! check convergence
|
|
! compute v1 = r0/||r0||_2
|
|
|
|
if (debug_level >= psb_debug_ext_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' restart: ',itx,it
|
|
it = 0
|
|
call psb_geaxpby(cone,b,czero,v(:,1),desc_a,info)
|
|
if (info /= psb_success_) then
|
|
info=psb_err_from_subroutine_non_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
end if
|
|
|
|
call psb_spmm(-cone,a,x,cone,v(:,1),desc_a,info,work=aux)
|
|
if (info /= psb_success_) Then
|
|
info=psb_err_from_subroutine_non_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
End If
|
|
|
|
rs(1) = psb_genrm2(v(:,1),desc_a,info)
|
|
rs(2:) = czero
|
|
if (info /= psb_success_) Then
|
|
info=psb_err_from_subroutine_non_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
end if
|
|
scal=done/rs(1) ! rs(1) MIGHT BE VERY SMALL - USE DSCAL TO DEAL WITH IT?
|
|
|
|
if (debug_level >= psb_debug_ext_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' on entry to amax: b: ',Size(b),rs(1),scal
|
|
|
|
!
|
|
! check convergence
|
|
!
|
|
if (istop_ == 1) then
|
|
rni = psb_geamax(v(:,1),desc_a,info)
|
|
xni = psb_geamax(x,desc_a,info)
|
|
errnum = rni
|
|
errden = (ani*xni+bni)
|
|
else if (istop_ == 2) then
|
|
rni = psb_genrm2(v(:,1),desc_a,info)
|
|
errnum = rni
|
|
errden = bn2
|
|
endif
|
|
if (info /= psb_success_) then
|
|
info=psb_err_from_subroutine_non_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
end if
|
|
|
|
if (errnum <= deps*errden) exit restart
|
|
|
|
if (itrace_ > 0) &
|
|
& call log_conv(methdname,me,itx,itrace_,errnum,errden,deps)
|
|
|
|
v(:,1) = v(:,1) * scal
|
|
|
|
if (itx >= litmax) exit restart
|
|
|
|
!
|
|
! inner iterations
|
|
!
|
|
|
|
inner: Do i=1,nl
|
|
itx = itx + 1
|
|
|
|
call prec%apply(v(:,i),w1,desc_a,info)
|
|
Call psb_spmm(cone,a,w1,czero,w,desc_a,info,work=aux)
|
|
!
|
|
|
|
do k = 1, i
|
|
h(k,i) = psb_gedot(v(:,k),w,desc_a,info)
|
|
call psb_geaxpby(-h(k,i),v(:,k),cone,w,desc_a,info)
|
|
end do
|
|
h(i+1,i) = psb_genrm2(w,desc_a,info)
|
|
scal=done/h(i+1,i)
|
|
call psb_geaxpby(scal,w,czero,v(:,i+1),desc_a,info)
|
|
do k=2,i
|
|
call crot(1,h(k-1,i),1,h(k,i),1,real(c(k-1)),s(k-1))
|
|
enddo
|
|
|
|
rti = h(i,i)
|
|
rti1 = h(i+1,i)
|
|
call crotg(rti,rti1,tmp,s(i))
|
|
c(i) = cmplx(tmp,szero)
|
|
call crot(1,h(i,i),1,h(i+1,i),1,real(c(i)),s(i))
|
|
h(i+1,i) = czero
|
|
call crot(1,rs(i),1,rs(i+1),1,real(c(i)),s(i))
|
|
|
|
if (istop_ == 1) then
|
|
!
|
|
! build x and then compute the residual and its infinity norm
|
|
!
|
|
rst = rs
|
|
xt = czero
|
|
call ctrsm('l','u','n','n',i,1,cone,h,size(h,1),rst,size(rst,1))
|
|
if (debug_level >= psb_debug_ext_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' Rebuild x-> RS:',rst(1:nl)
|
|
do k=1, i
|
|
call psb_geaxpby(rst(k),v(:,k),cone,xt,desc_a,info)
|
|
end do
|
|
call prec%apply(xt,desc_a,info)
|
|
call psb_geaxpby(cone,x,cone,xt,desc_a,info)
|
|
call psb_geaxpby(cone,b,czero,w1,desc_a,info)
|
|
call psb_spmm(-cone,a,xt,cone,w1,desc_a,info,work=aux)
|
|
rni = psb_geamax(w1,desc_a,info)
|
|
xni = psb_geamax(xt,desc_a,info)
|
|
errnum = rni
|
|
errden = (ani*xni+bni)
|
|
!
|
|
|
|
else if (istop_ == 2) then
|
|
!
|
|
! compute the residual 2-norm as byproduct of the solution
|
|
! procedure of the least-squares problem
|
|
!
|
|
rni = abs(rs(i+1))
|
|
errnum = rni
|
|
errden = bn2
|
|
endif
|
|
|
|
If (errnum <= deps*errden) Then
|
|
|
|
if (istop_ == 1) then
|
|
x = xt
|
|
else if (istop_ == 2) then
|
|
!
|
|
! build x
|
|
!
|
|
call ctrsm('l','u','n','n',i,1,cone,h,size(h,1),rs,size(rs,1))
|
|
if (debug_level >= psb_debug_ext_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' Rebuild x-> RS:',rs(1:nl)
|
|
w1 = czero
|
|
do k=1, i
|
|
call psb_geaxpby(rs(k),v(:,k),cone,w1,desc_a,info)
|
|
end do
|
|
call prec%apply(w1,w,desc_a,info)
|
|
call psb_geaxpby(cone,w,cone,x,desc_a,info)
|
|
end if
|
|
|
|
exit restart
|
|
|
|
end if
|
|
|
|
if (itrace_ > 0) &
|
|
& call log_conv(methdname,me,itx,itrace_,errnum,errden,deps)
|
|
|
|
end do inner
|
|
|
|
if (istop_ == 1) then
|
|
x = xt
|
|
else if (istop_ == 2) then
|
|
!
|
|
! build x
|
|
!
|
|
call ctrsm('l','u','n','n',nl,1,cone,h,size(h,1),rs,size(rs,1))
|
|
if (debug_level >= psb_debug_ext_) &
|
|
& write(debug_unit,*) me,' ',trim(name),&
|
|
& ' Rebuild x-> RS:',rs(1:nl)
|
|
w1 = czero
|
|
do k=1, nl
|
|
call psb_geaxpby(rs(k),v(:,k),cone,w1,desc_a,info)
|
|
end do
|
|
call prec%apply(w1,w,desc_a,info)
|
|
call psb_geaxpby(cone,w,cone,x,desc_a,info)
|
|
end if
|
|
|
|
end do restart
|
|
if (itrace_ > 0) &
|
|
& call log_conv(methdname,me,itx,1,errnum,errden,deps)
|
|
|
|
call log_end(methdname,me,itx,errnum,errden,deps,err=derr,iter=iter)
|
|
|
|
if (present(err)) then
|
|
err = derr
|
|
end if
|
|
|
|
|
|
deallocate(aux,h,c,s,rs,rst, stat=info)
|
|
if (info == psb_success_) call psb_gefree(v,desc_a,info)
|
|
if (info == psb_success_) call psb_gefree(w,desc_a,info)
|
|
if (info == psb_success_) call psb_gefree(w1,desc_a,info)
|
|
if (info == psb_success_) call psb_gefree(xt,desc_a,info)
|
|
if (info /= psb_success_) then
|
|
info=psb_err_from_subroutine_non_
|
|
call psb_errpush(info,name)
|
|
goto 9999
|
|
end if
|
|
|
|
! restore external global coherence behaviour
|
|
call psb_restore_coher(ictxt,isvch)
|
|
|
|
call psb_erractionrestore(err_act)
|
|
return
|
|
|
|
9999 continue
|
|
call psb_erractionrestore(err_act)
|
|
if (err_act == psb_act_abort_) then
|
|
call psb_error()
|
|
return
|
|
end if
|
|
return
|
|
|
|
|
|
contains
|
|
|
|
subroutine crot( n, cx, incx, cy, incy, c, s )
|
|
!
|
|
! -- lapack auxiliary routine (version 3.0) --
|
|
! univ. of tennessee, univ. of california berkeley, nag ltd.,
|
|
! courant institute, argonne national lab, and rice university
|
|
! october 31, 1992
|
|
!
|
|
! .. scalar arguments ..
|
|
integer incx, incy, n
|
|
real(psb_spk_) c
|
|
complex(psb_spk_) s
|
|
! ..
|
|
! .. array arguments ..
|
|
complex(psb_spk_) cx( * ), cy( * )
|
|
! ..
|
|
!
|
|
! purpose
|
|
! == = ====
|
|
!
|
|
! zrot applies a plane rotation, where the cos (c) is real and the
|
|
! sin (s) is complex, and the vectors cx and cy are complex.
|
|
!
|
|
! arguments
|
|
! == = ======
|
|
!
|
|
! n (input) integer
|
|
! the number of elements in the vectors cx and cy.
|
|
!
|
|
! cx (input/output) complex*16 array, dimension (n)
|
|
! on input, the vector x.
|
|
! on output, cx is overwritten with c*x + s*y.
|
|
!
|
|
! incx (input) integer
|
|
! the increment between successive values of cy. incx <> 0.
|
|
!
|
|
! cy (input/output) complex*16 array, dimension (n)
|
|
! on input, the vector y.
|
|
! on output, cy is overwritten with -conjg(s)*x + c*y.
|
|
!
|
|
! incy (input) integer
|
|
! the increment between successive values of cy. incx <> 0.
|
|
!
|
|
! c (input) double precision
|
|
! s (input) complex*16
|
|
! c and s define a rotation
|
|
! [ c s ]
|
|
! [ -conjg(s) c ]
|
|
! where c*c + s*conjg(s) = 1.0.
|
|
!
|
|
! == = ==================================================================
|
|
!
|
|
! .. local scalars ..
|
|
integer i, ix, iy
|
|
complex(psb_dpk_) stemp
|
|
! ..
|
|
! .. intrinsic functions ..
|
|
! ..
|
|
! .. executable statements ..
|
|
!
|
|
if( n <= 0 ) return
|
|
if( incx == 1 .and. incy == 1 ) then
|
|
!
|
|
! code for both increments equal to 1
|
|
!
|
|
do i = 1, n
|
|
stemp = c*cx(i) + s*cy(i)
|
|
cy(i) = c*cy(i) - conjg(s)*cx(i)
|
|
cx(i) = stemp
|
|
end do
|
|
else
|
|
!
|
|
! code for unequal increments or equal increments not equal to 1
|
|
!
|
|
ix = 1
|
|
iy = 1
|
|
if( incx < 0 )ix = ( -n+1 )*incx + 1
|
|
if( incy < 0 )iy = ( -n+1 )*incy + 1
|
|
do i = 1, n
|
|
stemp = c*cx(ix) + s*cy(iy)
|
|
cy(iy) = c*cy(iy) - conjg(s)*cx(ix)
|
|
cx(ix) = stemp
|
|
ix = ix + incx
|
|
iy = iy + incy
|
|
end do
|
|
end if
|
|
return
|
|
end subroutine crot
|
|
!
|
|
!
|
|
subroutine crotg(ca,cb,c,s)
|
|
complex(psb_spk_) ca,cb,s
|
|
real(psb_spk_) c
|
|
real(psb_spk_) norm,scale
|
|
complex(psb_spk_) alpha
|
|
!
|
|
if (cabs(ca) == 0.0) then
|
|
!
|
|
c = 0.0d0
|
|
s = (1.0,0.0)
|
|
ca = cb
|
|
return
|
|
end if
|
|
!
|
|
|
|
scale = cabs(ca) + cabs(cb)
|
|
norm = scale*sqrt((cabs(ca/cmplx(scale,0.0)))**2 +&
|
|
& (cabs(cb/cmplx(scale,0.0)))**2)
|
|
alpha = ca /cabs(ca)
|
|
c = cabs(ca) / norm
|
|
s = alpha * conjg(cb) / norm
|
|
ca = alpha * norm
|
|
!
|
|
|
|
return
|
|
end subroutine crotg
|
|
End Subroutine psb_crgmres
|